View
37
Download
3
Category
Preview:
DESCRIPTION
Continuous Symmetry and Chirality Measures. David Avnir Institute of Chemistry The Hebrew University of Jerusalem. Harvard, Boston, January 28, 2013. “Near” C 2 symmetry: HIV Protease mutant V82A complexed with A77 inhibitor. - PowerPoint PPT Presentation
Citation preview
Continuous Symmetry and Chirality Measures
David Avnir
Institute of ChemistryThe Hebrew University of JerusalemHarvard, Boston, January 28, 2013
Near C2 symmetry: HIV Protease mutant V82A complexed with A77 inhibitorWhat, quantitatively, is the C2 symmetry content of that protein?
Gradual changing chirality and C2-ness in aggregatesIs it possible to quantify these changes?
Since achirality relates to symmetry, similar questions pop up also in the context of chirality:By how much is one molecule more chiral than the other?
In fact, asymmetry and chirality are very common:
Given a sufficiently high resolution in space or time it is quite difficult to find a fully symmetric, achiral molecule.
Consider watching methane on a vibrational time-scale: Only one in zillion frames will show the following:
Given a sufficiently high resolution in space or time it is quite difficult to find a fully symmetric, achiral molecule
Spatial resolutions: Often, symmetry is lost at the condensed phase:# An adsorbed molecule# A matrix-entrapped molecule# A molecule packed in the crystal# A molecule in the glassy state# A molecule within a cluster
A methodology is needed in order to quantify the degree of symmetry and the degree of chirality:
# Comparing different molecules# Following changes within a single molecule
The proposed methodology for a symmetry-measure design:
Find the minimal distance between the original structure, and the one obtained after the G point-group symmetry is operated on it.
The continuous symmetry measure* The scale is 0 - 1 (0 - 100): The larger S(G) is, the higher is the deviation from G-symmetry
: The original structure: The symmetry-operated structureN : Number of verticesd : Size normalization factorH. Zabrodsky
_1204988856.unknown
_1142321119.unknown
Measuring the degree of C3-ness (S(C3)) of a triangleCh. Dryzun
All three triangles are superimposed. The set of 9 points is C3-symmetric. Its blues average is a C3-symmetric triangleThe measure is the collection of distances between the blue and the (original) red
G: The achiral symmetry point group which minimizes S(G)Achiral molecule: S(G) = 0
The more chiral the molecule is, the higher is S(G) S(G) as a continuous chirality measure
The Continuous Shape MeasureS. Alvarez, P. Alemany* The CSM estimates the distance to an a-priori unknown shape with the desired symmetry
* The Shape Measure estimates the minimal distance to a specific pre-selected shape (any shape)
* For ML6:# Shape: What is the degree of ML6-octahedricity (S(L6-Oh))?# Symmetry: What is the degree of Oh-ness (S(Oh))? D4h-ness (S(D4h)? And of S(D2h)?
* The measure is a global structural parameter: It takes into account all bond angles and bond lengths
* A full profile of symmetry and chirality values is obtained
* All values are comparable either within the same molecule or between different ones
* The computational tools are efficient
* Analytical solutions have been obtained for many types of symmetry * The shape of the nearest symmetric object is an outcome
* The measure is well behaved, and its correlations with physical/chemical parameters agree with intuition
Some properties of the symmetry measure
Planar square D4h
The full scale of the CSM
The most chiral monodentate complex
Trends within families and classifications
Symmetry maps
The symmetry map of 13,000 transition metal ML4 complexesS. Alvarez, P. Alemany, JACS 2004
CuCl42-: The tetrahedral to planar-square symmetry map and pathwayS(Td)S(D4h)S. Keinan
Several possible pathways for this transformationSpreadTwistCompression
The tetrahedral to planar-square transformationCuCl42-S(Td)S(D4h)
Minimal energy and minimal symmetry values coincideS(D4h)
Tetracoordinated Bis-Chelate Metal ComplexesM(L-L')2: The [M(bipy)2] family L-M-L bond angles: # Spread From 90 to 109.4#Two Twist pathways: The bidentate nature is introduced by keeping the two opposite L-M-L bond angles constant at typical 82 and 73Twist
We (mainly S. Alvarez) analyzed similarly all MLn families with n from 4 to 104Chem. Eur. J., 10, 190-207 (2004).5J. Chem. Soc., Dalton Trans., 3288-3303 (2000). 6New J. Chem., 26, 996-1009 (2002). 7Chem. Eur. J., 9, 1281-1295 (2003).8Chem. Eur. J., 11, 1479 (2005).9Inorg. Chem., 44, 6939-6948 (2005).10Work in progress
Symmetry or chirality as reaction coordinates
Stone-Wales Enantiomerizations in FullerenesY. Pinto, P. Fowler (Exeter)
Hckel energy changes along the enantiomerization
The sensitivity of energy/chirality dependence on the size of the fullerene
Temperature and pressure effects on symmetry and chirality
Temp (oK)S(Oh)Data: Wei, M. & Willett, R.D. Inorg. Chem. (1995) 34, 3780. Analysis: S. KeinanChanges in the degree of octahedricity with temperatureCuCl64-
Low QuartzSiO2, P3221Temperature and pressure effects on the chirality and symmetry of extended materials: Quartz
The building blocks of quartz SiO4Si(OSi)4SiSi4-O(SiO3)4-
Combining temperature and pressure effects through symmetry analysisbS(C2) of a four tetrahedra unit: A measure of helicityA correlation between global and specific geometric parameters
Predicting the high pressure symmetry behavior of quartz based on the isostrucutral GeO2D. Yogev-Einot , D. Avnir; Acta Cryst. (2004) B60 163-173
The building blocks of quartz: All are chiral!SiO4Si(OSi)4SiSi4-O(SiO3)4-
M. Pinsky et al, Statistical analysis of the estimation of distance measures J. Comput. Chem., 24, 786796 (2003)
How small can the measure be and still indicate chirality?The error bar
# Typical limit: In quartz, S(Chir) of SiO4 = 0.0007 # For S values near zero, the error bar is not symmetric: The + and - are different. # If the lower bound of S touches 0.00000, then the molecule is achiral.
The optical rotation of quartz Le Chatelier, H. Com. Rend de I'Acad Sciences 1889, 109, 264.
115 years later: Interpretation and exact match with quantitative chirality changesCrystallography: Kihara, 1990. Analysis: D. Yogev-EinotSiSi4
Correlations between continuous symmetry and spectral properties
S(Td)max d-d (cm-1)Jahn-Teller effects and symmetry:The d-d splitting in Cu complexesData: Halvorson, 1990. Analysis: S. Keinan
Changes in transition probability as a function of octahedricityCuN4O2 Chromophores:S(Oh) [cm-1M-1]Data: P. Comba, 1999+2H2O
Degree of allowedness of ESR transition as a function of the degree of tetrahedricity
Maximal and minimal shielding in AB4 speciesSymmetry effects on NMR chemical shielding
Current wisdom:But how does the shielding change when the symmetry changes continuously?
350010203040CSA (ppm)S(D4h) deviation from planarityCSA vs. S(D4h)200 randomly distorted SiH4All 29Si NMR properties were calculated using Gaussian98, B3LYP/6-31G* and GIAOA. Steinberg, M. Karni
Correlation between symmetry/chirality and chemical recognition
* Chromatography* Catalysis* Enzymatic activity
The pioneering work of Gil-Av on chiral separations of helicenesE. Gil-Av, F. Mikes, G. Boshart, J. Chromatogr, 1976, 122, 205A pair of enantiomers of a [6]-heliceneSilica derivatized with a chiral silylating agent
Enantioselectivity of a chiral chormatographic column towards helicenesIs there a relation between this behavior and the degree of chirality of helicenes?
The chiral separation of helicenes on Gil-Avs column is dictated by their degree of chiralityO. KatzenelsonTetrahedron-Asymmetry, 11, 2695 (2000)Gil-AvQuantitative chirality
Catalysis
Catalytic Chiral Diels-Alder ReactionData: Davies, 1996. Analysis: Lipkowitz, Katzenelson
The nearest symmetry plane of the catalystn = 1
The enantiomeric excess of the product as a function of the degree of chirality of the catalystLipkowitz, JACS 123 6710 (2001)
Which smallest fragment carries the essential chirality?S. Alvarez
The smallest fragment which carries the essential chirality for catalysis
Prediction 1: Replace the exocyclic ring with C=O or C=CH2 to get good homologue catalysts
Prediction 2: Increase the twist angle
Enzymatic activity
Trypsin inhibitorsS. Keinan JACS 98
Attempt to find a correlation between the inhibition constant and the chirality of the whole inhibitorNo correlation; but
The correlation follows the degree of chirality but not the length of the alkyl chainCorrelation between inhibition and the chirality of the pharmacophor
Inhibition of acetylcholine esterase by chiral organophosphates
Ala82Asn83Ile84Gly50HIV protease complexed with A77 inhibitorHIV protease-drug complex C2-symmetric color map
F: Native HIV-protease inhibitorsE: Native HIV-protease inhibitor A77J: V82A mutant HIV-protease inhibitor A77
Free energy of inhibitors binding vs. their C2-symmetry change
Given a sufficiently high resolution in space or in time, nothing is symmetric, everything is chiral
Our web-site (beta)http://chirality.ch.huji.ac.il/ or http://www.csm.huji.ac.il/
The J. Am. Chem. Soc. Series:
114, 7843 (1992)115, 8278 (1993)117, 462 (1995)120, 6152 (1998)122, 4378 (2000)123, 6710 (2001)125, 4368 (2003)126, 1755 (2004)
LiteratureRecent:
A. Steinberg et al, "Continuous Symmetry Analysis of NMR Chemical Shielding Anisotropy, Chem. Eur. J., 12, 8534 8538 (2006)
D. Yogev-Einot et al, "The temperature-dependent optical activity of quartz: from Le Chatelier to chirality measures, Tetrahedron: Asymmetry 17, 2723 2725 (2006)
Mark Pinsky et al, "Symmetry operation measures, J. Comput. Chem., 2007
*****************************************************************************
Recommended